I would like to collaborate with other educators/mathematicians/statisticians on an article about different interpretations of and experiences with quantitative reasoning courses across different institutions. I am interested in applications of teaching research (teaching experiments, research cycles, zones of proximal development, etc.) to QR courses. As educators we sometimes forget that we are also teaching researchers, a role that is not always realized but is practiced by default. We design courses and assessment tools, we collect student data, we analyze student feedback and our own designs to adjust our courses to improve the attainment of goals that are set by us, or by our colleagues. More often than not, we might not go the extra few steps to properly formulate our hypotheses, conduct our experiments as scientifically as possible, and organize and publish our work. Most of us have pure mathematics/statistics research interests, and concentrate our research skills and products towards those areas, discounting the research we automatically undertake as educators. I, myself, was only recently made aware of the official framework of teaching research when I took on the role of editor on a soon to be published book on the topic by Bronislaw Czarnocha and Vrunda Prabhu, among other contributors. I have also contributed a chapter in the book describing the Science/Mathematics Interdisciplinary Workshop at Hostos Community College. This workshop was developed jointly by me, Yoel Rodriguez and Francisco Fernandez (also co-authors of the chapter).

The educational philosophy and the institutional structure of Eugenio Maria de Hostos Community College (HCC) is driven by its history, its student population and its overarching mission: Consistent with the mission of The City University of New York (CUNY) to provide access to higher education for all who seek it, Eugenio María de Hostos Community College was established in the South Bronx to meet the higher educational needs of people from this and similar communities who historically have been excluded from higher education. The mission of Eugenio María de Hostos Community College is to offer access to higher education leading to intellectual growth and socio-economic mobility through the development of linguistic, mathematical, technological, and critical thinking proficiencies needed for lifelong learning and for success in a variety of programs including careers, liberal arts, transfer, and those professional programs leading to licensure (Hostos, 2014) The college takes great pride in its historical role in cultivating students from diverse ethnic, racial, cultural and linguistic backgrounds, ― "An integral part of fulfilling its mission is to provide transitional language instruction for all English-as-a-Second-Language learners," as well as a variety of different specialized "education offerings to foster a multicultural environment for all students." (Hostos, 2014) To further advance the college's goal and to foster a rich learning environment, equipping students with necessary tools and affording them accessibility to a wide spectrum of opportunities, HCC, together with some of its senior CUNY college partners, currently offers several joint-degree/dual-admission programs: A.A./B.A in Criminal Justice, jointly with John Jay College, A.S./B.S. in Forensic Science, also jointly with John Jay College, and several A.S./B.E. programs, jointly with City College (CCNY). The latter include degrees in Mechanical, Civil, Chemical, Electrical and Environmental Engineering. Additional joint A.S./B.S. programs, in Chemistry, Earth Science and Biology, are presently being developed in association with Lehman College with the assistance of an NSF grant, and will be available to HCC students soon (Project SEED, 2012). Unlike articulation agreements, the current HCC-CCNY engineering partnerships are jointly registered, dual admission programs designed to meet the licensure guidelines of the Accreditation Board for Engineering and Technology (ABET).

The most common difficulties found among HCC students taking science courses, as is the situation nationwide, are inadequate problem-solving foundations, lack of abstract-analysis skills and a lack of sufficient ability to make connections with previous knowledge, specifically, with concepts in mathematics such as trigonometry, geometric and algebraic operations on vectors, and an adequate understanding of introductory calculus (Zumdahl A266). Some of these students have never taken physics, or any science course, for that matter, during their previous educational endeavours. As a result, by the time they take the course, they often already have come to “dislike” physics, and feel frustrated and discouraged because they do not understand it. Furthermore, even when they understand the concepts, they find it very difficult to solve physics problems because of lack of visualization and critical thinking skills. These could be some of the reasons why many students do not consider science careers as professional options despite the great demand in the United States for potential scientists (AACU 9; Mervis, “NIH Told” 328; Mervis, “NIH Wants” 1119; Rochin and Mello 305), as well as mathematics and science middle school and high school teachers. To address this problem, among others, the Natural Sciences Department and the Mathematics Department, with the help of the Office of Academic Affairs at Hostos, created and began offering the Intersession Science Institute in the winter of 2010. This institute was tailored primarily for students enrolled in one of the four initial Hostos Engineering programs (Civil, Chemical, Electrical and Mechanical), but is open to all students who intend to take a Physics or Chemistry course for their respective degrees.

Here's a link to a partial version of the chapter:

https://www.researchgate.net/publication/267336448_CHAPTER_4.4_BRIDGING_THEORY_AND_APPLICATIONS_IMPROVING_STUDENTS%27_MATHEMATICAL_PROFICIENCY_FOR_THE_PHYSICAL_SCIENCES_WITH_EMPHASIS_ON_PHYSICS

The book, still at the final editing stage, is "the story of the interaction between Teaching-Research and Creativity, both mathematical and pedagogical. Creativity had explicitly been introduced into Teaching-Research NYCity Model by Vrunda Prabhu through the Bisociation theory of Arthur Koestler formulated in his Act of Creation (1964), which was found to correspond to Prabhu’s spontaneous organization of the Learning Environment in her classes of mathematics at the Bronx Community College of CUNY. Bisociation, that is, the creative leap of insight that connects previously unconnected frames of reference, allowing the reality to be experienced in several planes at once – the definition of an Aha moment or the Eureka experience - defines also a bisociative framework that makes bisociation possible. It is the framework composed of at least two unconnected frames of reference. Teaching-Research, the integration of two “habitually unconnected” frames of reference, teaching and research, is therefore such a bisociative framework which particularly strongly promotes pedagogical and mathematical creativity in the classroom. It is fascinating to mention that the same bisociative theory recently became the basis for the Computer Creativity, a new domain in Artificial Intelligence (Berthold, 2012). Collaborative investigations into Human and Computer Creativity based on the bisociation theory promise to be a fascinating “bisociative” endeavour. The story of the book has many interweaving themes, some of them explicit and some of them implicit. The explicit themes are formulated by the guiding theme of each unit and their chapters. The structure and organization of the volume introduces the reader to basic TR ideas ...that are applied to the design of instruction in the context of Creative Learning Environment in the classroom... We apply TR methods to the creation of several learning trajectories in Arithmetic and Algebra... we demonstrate the creative power of different bisociative frameworks through TR collaborations of mathematics with different academic disciplines. [Another unit] discusses different roles of a concept map, a pedagogical conceptual tool, which we found very useful in TR work as manifestly evident throughout the book. We close the book with a unit that reports on and analyses two different Professional Developments of Teacher-Researchers, in Tamil Nadu, India and in Europe, each creating a developmental model of a teacher-researcher adapted to the conditions of teaching and learning.

The implicit themes, on the other hand, crisscross different chapters in different units. One of the central such implicit themes is, of course, the relation between practice and. theory and research results. Many aspects of this relationship are weaved in throughout the book. Application of learning theories to classroom practice, derivation of research hypotheses from pilot teaching-experiments. Special attention was given to the presentation and weaving in the bisociation theory into the basic fabric of mathematics education research and practice The relationship between learning mathematics and learning language has been one of the more pressing themes given that our colleges Hostos CC and Bronx CC are minority colleges. Of course, the themes of creativity, discovery and understanding with related methodological comments reappear freely in many different contexts and chapters. Teachers-researchers are the only ones who can establish fruitful relationships between the theory and research results underlying the approach of Learning Trajectories, the backbone of the curriculum design, and their practical classroom utilization, assessment and refinement. Yet in order to fully use the potential of the teaching-research for classroom activity, teachers need to be awarded the systematic time for reflection (see Chapter 6.2). "

Currently, I am very heavily involved in applying the above theory to the subject of quantitative reasoning and literacy, and am very curious about similar projects that other educators might be undertaking for a collaborative effort on a QRTR theory and practice investigation. I am currently teaching and developing the following courses:

Quantitative Reasoning 1: This course is designed to help students gain an understanding of fundamental numerical and quantitative skills and their application to everyday life. The focus will be on applying basic mathematical concepts to solve real-world problems, and to develop skills in interpreting and working with data in order that students become able to function effectively as professionals and engaged citizens. Topics will include problem-solving and back-of-the-envelope calculations, unit conversions and estimation, percentages and compound interest, linear and other models, data interpretation, analysis and visualization, basic principles of probability, and an introduction to quantitative research and statistics. Another important objective of the course is a clear introduction to and a development of appropriate working knowledge of MS-Excel as well as some of the software’s most common applications in a variety of contexts.

Quantitative Reasoning 2 - Quantitative Research Methods: This course is aimed at developing students’ ability to (i) identify a well-formed data-based research question, (ii) find, analyze and present the relevant quantitative information in support of the pertinent argument, and (iii) to compile all results and construct a sophisticated data analysis project. Building upon QR1’s numerical and quantitative skills, this course will focus on quantitative research methods and skills, including elements of statistical analysis and their application to business and social sciences. Students will develop an ability to identify, understand, and critique primary and secondary research in industry, scholarly, government, and other specialized publications; they will also gain familiarity with the use of large data sets.

Chapter CHAPTER 4.4 BRIDGING THEORY AND APPLICATIONS: IMPROVING STUD...